Egyptian Method of Multiplication

Date: 6/26/96 at 20:15:34
From: Doctor Jodi
Subject: Re: Egyptian Method of Multiplication
Hi Carrie! Yes, we have.... Here's a description of the method, from
http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Babylonian_and_Egyptian.html
Unlike the Greeks, who thought abstractly about mathematical ideas,
the Egyptians were only concerned with practical arithmetic. In fact
the Egyptians probably did not think of numbers as abstract quantities
but always thought of a specific collection of 8 objects when 8 was
mentioned. To overcome the deficiencies of their system of numerals
the Egyptians devised cunning ways around the fact that their numbers
were unsuitable for multiplication, as is shown in the Rhind papyrus
which date from about 1700 BC.
The Rhind papyrus recommends that multiplication be done in the
following way. Assume that we want to multiply 41 by 59. Take 59 and
add it to itself, then add the answer to itself and continue:
41 59
______________
1 59
2 118
4 236
8 472
16 944
32 1888
______________
Since 64 > 41, there is no need to go beyond the 32 entry. Now go
through a number of subtractions
41 - 32 = 9, 9 - 8 = 1, 1 - 1 = 0
to see that 41 = 32 + 8 + 1. Next check the numbers in the righthand
column corresponding to 32, 8, 1 and add them.
59
______________
1 59 X
2 118
4 236
8 472 X
16 944
32 1888 X
______________
2419
Notice that the multiplication is achieved with only additions; notice
also that this is a very early use of binary arithmetic. Reversing the
factors we have
59 41
______________
1 41 X
2 82 X
4 16
8 328 X
16 656 X
32 1312 X
_______________
2419
Enjoy! Let us know if you need more help.
-Doctor Jodi, The Math Forum
Check out our web site! http://mathforum.org/dr.math/